Integrated Square Error Asymptotics for Supersmooth Deconvolution

Hajo Holzmann and Leif Boysen

Scandinavian Journal of Statistics, 2006, vol. 33, issue 4, 849-860

Abstract: Abstract. We derive the asymptotic distribution of the integrated square error of a deconvolution kernel density estimator in supersmooth deconvolution problems. Surprisingly, in contrast to direct density estimation as well as ordinary smooth deconvolution density estimation, the asymptotic distribution is no longer a normal distribution but is given by a normalized chi‐squared distribution with 2 d.f. A simulation study shows that the speed of convergence to the asymptotic law is reasonably fast.

Date: 2006
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